Elliptic curve isogeny class with LMFDB label 48552.w (Cremona label 48552r)

• Label: 48552.w
• Number of curves: $1$
• Conductor: $48552$
• CM: no
• Rank: $1$

Rank

The elliptic curve 48552.w1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1 + T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 48552.w do not have complex multiplication.

Modular form 48552.2.a.w

Elliptic curves in class 48552.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
48552.w1	48552r1	\([0, 1, 0, -48648, -4148991]\)	\(-9528223648000/7411887\)	\(-9904771426032\)	\([]\)	\(133056\)	\(1.4251\)	\(\Gamma_0(N)\)-optimal